In a good hit, a baseball and bat are in contact with each other for about 1 millisecond. In the first game of the 2012 World Series, Tigers pitcher Justin Verlander threw a 100-mph pitch to the Giants' Pablo Sandoval. Sandoval's hit returned the ball directly back at Verlander at 70 mph. Calculate the average force of the bat on the ball, during the contact. Round the final answer to the nearest whole number.

Explanation:

100 mph = 100 x 1760 x 3 / ( 60 x 60 )

= 146.67 ft / s

70 mph = 70 x 1760 x 3 / ( 60 x 60 )

= 102.67 ft/s

Let mass of the ball = m .

The ball which was moving with a velocity of 146.67 ft/s is turned back by the action of force of bat on the ball and it moved in opposite direction with velocity of - 102.67 ft/s ( - ve sign due to reversed direction )

If m be the mass of ball

change in momentum = m x 146.67 - ( - m x 102.67 )

=  m x 146.67 +  m x 102.67

= 249.34 m

Change in momentum = impulse = force x time

Putting the given values

249.34 m = force x 1 x 10⁻³ ( time = 10⁻³ s )

force = 249.34 m x 10³ poundal .

Here m is mass of the ball in lb .

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